AERN-RnToRm
Version 0.3.0.2 revision 0 uploaded by MichalKonecny.
Package meta
- Synopsis
- polynomial function enclosures (PFEs) approximating exact real functions
- Description
AERN-RnToRm provides datatypes and abstractions for approximating functions of type
D -> R^m
whereD
is a bounded interval inR^n
with non-empty interior.Abstractions are provided via 4 type classes:
ERUnitFnBase: generalises polynomials with floating point coefficients.
ERFnApprox: generalises functions enclosures on a certain unspecified domain.
ERUnitFnApprox (extends ERFnApprox): generalises function graph enclosures on the domain
[-1,1]^n
.ERFnDomApprox (extends ERFnApprox): generalises function enclosures over a specified and queriable domain box (an instance of class DomainBox).
At all levels, all field operations are supported as well as some elementary operations, namely exp, sin and cos. Log and sqrt are planned to be added soon. End users are expected to work only with implementations of ERFnDomApprox.
Implementations of ERUnitFnBase:
ERChebPoly
By using the Chebyshev basis on domain
[-1,1]^n
, we gain simple and optimally rounding degree reduction as well as relatively simple handling of rounding in other operations.Implementations of ERUnitFnApprox:
ERFnInterval
Implementations of ERFnDomApprox:
ERFnDomTranslApprox: builds a basic implementation using an instance of ERUnitFnApprox.
ERFnTuple: extends another implementation of ERFnDomApprox to work with lists of functions simultaneously.
ERFnDomEdgesApprox: separately enclose a function on its domain box as well as on all the domain's hyper-edges (including the corners) using another implementation of ERFnDomApprox.
ERFnPiecewise: allows the domain box to be bisected to an arbitrary finite depth and uses another implementation of ERFnDomApprox to approximate the function on each segment.
Simple examples of usage can be found in tests: Demo.hs.
- Author
- Michal Konecny (Aston University)
- Bug reports
- n/a
- Category
- Data, Math
- Copyright
- (c) 2007-2008 Michal Konecny
- Homepage
- n/a
- Maintainer
- mik@konecny.aow.cz
- Package URL
- n/a
- Stability
- experimental